Demographic rates of arthropods vectors of human pathogens, as poikilotherm organisms, are sensitive to changes in temperature and, in many cases, also in water availability . The proposed model approaches by a mechanistic point of view the causal chain linking environmental forcing variables to bio-demographic rates and population dynamics of An. gambiae s.s. The model allowed to perform a sensitivity analysis on the systematic change in temperature and precipitation at four different Kenyan sites characterized by different landscape, hydrology, climate and epidemiological pattern.
The first investigated site is Nairobi, characterized by a tropical climate modified by highlands (climatic zones 6 in the classification scheme of ). Temperatures are relatively low and the precipitation regime is characterized by two maxima in April and November. The site is currently classified as not prone to malaria epidemic, but an increase in temperatures is expected to contribute to make the Nairobi area more suitable to malaria . However, the contribution of rising temperature to vector population abundance appears to be important only for substantial temperature changes. In fact, results of our simulation show how the effect of a temperature increase of 1°C on mosquito development, survival and reproduction produces an adult population variation of +37%, that becomes +77% for +2°C, and +111% for +3°C. The contribution of mosquito abundance change to the local epidemiological pattern is quite difficult to infer. In the Nairobi area, a temperature increase could also give a more rapid sporogonic cycle. Biting rate is also expected to be affected by an increase of mosquito adult population abundance. Only a physiological-based mechanistic approach, considering the interaction among vector, pathogen and host, could highlight how such modification in the vectorial component may contribute to a change in the malaria prevalence.
A decrease in temperature could make the Nairobi area even more protected from malaria risk, as a result of the joint effect of temperature on both the key processes of vector population dynamics and maturation time of the parasite. The effect of negative variations in temperature has proved comparatively more important than the positive one, depleting the adult population of 31%, 56%, and 74% for thermal changes of -1, -2, and -3°C respectively. Furthermore, rainfall changes are expected to be much less important than thermal ones, at least in the tested range -20%/+ 20%. In any case, population dynamics display a positive linear pattern of variation with rainfall increase.
Nyabondo shows an equatorial climate modified by the influence of the lake Victoria (climatic zone 9 of ). The main climatic characteristics are high temperatures, high precipitation and absence of dry months . The area is prone to malaria epidemic due to abundant rainfall and temperature relatively close to the thermal optimum for biological performance of mosquito population (Figure 6a, b). Simulated scenarios show a gradual change in adult vector abundance with temperature rise, with an increase of 26%, 47% e 69% for +1, +2 and +3°C respectively. Sensitivity to temperature is less than in Nairobi, because the observed temperatures are closer to the optimum (Figure 6). Temperature decrease produces changes comparable with those obtained for Nairobi; such variation falls in the left trait of the distribution in Figure 6, where the slope of an interpolating curve is expected to be maximum. According to the model simulations, rainfall would not be a limiting factor, in agreement with values that are already high (1,285 mm) and well distributed along the year. In any case also for Nyabondo the abundance shows a direct linear positive correlation with the rainfall.
Kibwesi is prone to malaria epidemic and shows a tropical continental/semi-desert climate (zone 5 of ) with yearly precipitation below 500 mm. The pattern of variation of population dynamics is closely related to mean value of temperatures at this site that is very close to the optimum identified in Figure 6a, b. As a consequence, negative changes in temperature and most of the positive ones negatively effect population abundance. The system is sensitive to changes in rainfall, and the magnitude of variation is comparable with the values simulated for other sites, even if rainfall in this site is lower.
Malindi is characterized by the influence of the Indian Ocean that gives rise to a modified equatorial climate (climatic zones 1 of ) with high temperatures moderated by land and sea breeze (oceanic effect), very short or no dry season, two main precipitation maxima (May and November) and high humidity throughout the year. The pattern of response is highly dependent on the position of the average temperature with respect to distribution in Figure 6. Mosquito populations in Malindi are negatively affected by the super-optimal thermal conditions and population abundance may suffer of a further increase in temperature, while it may benefit from a temperature decrease. The gain in population abundance is proportional to the decrease of temperature at a rate that gradually decreases approaching optimal temperature.
The analysis here undertaken is site-specific because in this way we were able to feed the model with time series of real meteorological data deterministically perturbed. However, the pattern emerging from our simulations is of general validity (Figure 6a, b), and significantly follows the typical pattern of many biological response functions to temperature . This has two main implications. First, the three main bio-demographic rate functions (development, mortality and fecundity) are shaped in a way that population performance is optimized at a specific temperature and decreases departing from this thermal optimum. This is important for adaptation and influences habitat selection and species distribution. Second, the distribution in Figure 6a, b could be adopted as an index summarizing the integrated effects of temperatures on development, mortality and reproduction. This index expresses the An gambiae s.s. population potential productivity as function of average temperature conditions at local level. The index has a maximum at 25°C and non-linearly decreases toward zero approximately at 14-15°C, with a 10% mean rate of variation for each°C of temperature change. A decrease was also highlighted beyond the thermal optimum with a comparable but negative slope (-10%).
Population abundance typically increases linearly with rainfall variation (Figure 6c, d) throughout the whole precipitation range investigated and independently from the selected site. Symptoms of non-linearity, however, appear at the extremes of the studied range, suggesting that non-linear responses could take place outside the tested interval. The relatively uniform response of the system may be explained by the model parameterization. In fact, in all the sites the landscape is characterized by the same larval habitats features. This oversimplification is undoubtedly a limitation to achieve general conclusions, however it supports the idea that rainfall is a limiting factor and that, to some extent, the increase in water availability, in terms of surface for egg laying, promotes positive linear response in population productivity. In most of the cases such a change in population productivity resulted of 5-6% every 10% of precipitation increase.
The outcome of our analysis warns against any simplistic interpretation of the possible role of climatic variability on the malaria eco-epidemiology. In detail, the issue on climate change influences on vector population dynamics raised in our work leads to the arguments hereafter listed and briefly discussed.
a) Climate change analysis cannot be limited to the study of the temperature change effects. For many vector-borne diseases an increasing set of evidences show that other weather components, mainly precipitation and other hydrological variables, can significantly contribute to the system response. Furthermore, as discussed in the methodological section, analysis of climatic scenarios should be carried out taking into account that changes in air temperature and precipitation in tropical climates are correlated. More specifically temperature change results in variation in energy available for convective processes. This translates in changes in thunderstorms activity which in its turn can give rise to relevant feedbacks on surface energy balance and thermal regime [53, 54]. Biological response functions may further complicate this picture. As in the cases here analyzed, temperature and rainfall variations does not always drive the change in the system in the same direction, and the interaction between different physical and biological components of the landscape can give rise to complex and nonlinear patterns of change.
b) The obtained results provide important insight into the link between temperature change and responses of mosquito population dynamics. The presupposition of a linear response of the vectorial component in the malaria system to temperature changes is excessively simplistic. The reaction of population dynamics to temperature variation is non-linear, as expected considering the well know non-linear response to temperature of the demographic rate functions at the basis of population dynamics [29, 55, 56]. Such non-linearity also envisages a negative change in the population abundance for temperatures above the optimum temperature. This makes the hypothesized phenomenon of biological amplification of temperature effects  valid only for a limited range of temperatures. Moreover, even for climates that are more sensitive to temperature rises, as in the case of Nairobi, it is expected a maximum population abundance variation of 30% for every degree of temperature. This estimate is much smaller (one sixth) than the variation reported, for instance, by  which provide, on the basis of correlation analysis, an estimated increase of 100% every + 0.5°C.
c) The non-linearity in the temperature-dependent response of population dynamics and the correlation between air temperature and precipitation in tropical climates mean that no simple extrapolations can be done linking temperature raise and increase in distribution and abundance of An. gambiae s.s. populations. Therefore, projections on population distribution and productivity should be produced only in the light of the local climate as well as the physical and biological characteristics of the landscape involved in the maintenance of suitable habitats for mosquito. Referring to eco-epidemiological approach we also claim that population projections should take a great advantage from the contribution of process-based model simulation instead of relying on simple indexes and correlation analysis. But ultimately the response pattern of the malaria system can not be interpreted only in the light of the physical and biological factors because behavioural, socio-economic, control operation and other public health measures highly influence the spatial and temporal occurrence of the disease.
d) From the model simulations we derived a general pattern of temperature- and rainfall-dependent performance of An. gambiae s.s. populations productivity. This should help in defining the expected outcomes of climate variation at fine spatial scales, as well as the interpretation of heterogeneous distribution of mosquito and malaria prevalence in many eco-epidemiological contexts [57–59].
Despite the fact that the analysis is performed on a limited time period and for four sites only, nevertheless the proposed scenarios can be considered realistic and generalizable. From a meteorological point of view, results are supported by the fact that (i) the imposed daily air temperature variation is limited to about 2 standard deviations (see table 1) which represent a commonly accepted limit for strong anomalies , (ii) the reference stations selected represent four different climatic regimes for the Eastern African region, (iii) the reference period (27 years) is sufficiently long to capture a great part of the inter-yearly climatic variability that characterize the tropical regimes as a result of geographic, astronomic and circulation factors. Furthermore, the temperature-dependence of the bio-demographic rate functions used in the model, based on a literature review on this issue , provides biological foundation to the obtained population dynamics.
As a consequence of the above-mentioned elements the space and time domain of applicability of the results are considered relatively wide . To improve consistency and generality of the analyses performed, the following directions of development are of particular interest:
a) Improving model parameterization allowing to tackle morphological, pedological and hydrological characteristics of the landscape. By this point of view, the integration of ground measurements and remote-sensed data of land use, geomorphology and presence/time variability of small water reservoirs could be particularly important;
b) Obtaining suitable meteorological and hydrological datasets. The selected datasets are not completely satisfying with reference to average distance among stations and percentage of unavailable data. This highlights a possible problem for model management and show the need of a renewed attention to the quality and representativeness of observational data as crucial elements to express founded judgments on the effect of climate state and variability on tropical diseases;
c) Extending the analysis to other temporal and spatial scales. In a temporal perspective it might be interesting to focus on particular periods of the year to evaluate the effects of intra-annual variability of temperature and rainfall. Possible objectives of these studies should be, for example, the evaluation of the influence of specific patterns of rainfall and water resources availability on the rates of survival of mosquitoes during dry periods and the rates of re-colonization in areas with high seasonal rainfall variability. The model would also allow to assess the role of extreme and rare events (e.g., long periods of drought or heavy rainfall) or periodic events (e.g., El Niño-La Niña, the monsoon and their interactions) in conditioning mosquito population dynamics. In a spatial perspective it might be interesting to focus on mesoscale and macro-scale patterns.
d) Including in the model other malaria system components. The modular organization of the adopted modelling framework allows to gradually expand the model, integrating the modules for pathogen and human host and test their behaviour as well as the whole system responses with respect to climate variability.